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maint: Update copyright dates.
author John W. Eaton <jwe@octave.org>
date Wed, 22 Feb 2017 12:39:29 -0500
parents e9a0469dedd9
children 092078913d54
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1 ## Copyright (C) 1995-2017 Kurt Hornik
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {} {[@var{pval}, @var{t}, @var{df}] =} t_test_regression (@var{y}, @var{x}, @var{rr}, @var{r}, @var{alt})
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21 ## Perform a t test for the null hypothesis
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22 ## @nospell{@code{@var{rr} * @var{b} = @var{r}}} in a classical normal
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23 ## regression model @code{@var{y} = @var{x} * @var{b} + @var{e}}.
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24 ##
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25 ## Under the null, the test statistic @var{t} follows a @var{t} distribution
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26 ## with @var{df} degrees of freedom.
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27 ##
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28 ## If @var{r} is omitted, a value of 0 is assumed.
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29 ##
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30 ## With the optional argument string @var{alt}, the alternative of interest
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31 ## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null
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32 ## is tested against the two-sided alternative @nospell{@code{@var{rr} *
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33 ## @var{b} != @var{r}}}. If @var{alt} is @qcode{">"}, the one-sided
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34 ## alternative @nospell{@code{@var{rr} * @var{b} > @var{r}}} is used.
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35 ## Similarly for @var{"<"}, the one-sided alternative @nospell{@code{@var{rr}
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36 ## * @var{b} < @var{r}}} is used. The default is the two-sided case.
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37 ##
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38 ## The p-value of the test is returned in @var{pval}.
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39 ##
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40 ## If no output argument is given, the p-value of the test is displayed.
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41 ## @end deftypefn
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42
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43 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
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44 ## Description: Test one linear hypothesis in linear regression model
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45
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46 function [pval, t, df] = t_test_regression (y, x, rr, r, alt)
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47
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48 if (nargin == 3)
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49 r = 0;
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50 alt = "!=";
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51 elseif (nargin == 4)
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52 if (ischar (r))
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53 alt = r;
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54 r = 0;
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55 else
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56 alt = "!=";
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57 endif
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58 elseif (! (nargin == 5))
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59 print_usage ();
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60 endif
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61
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62 if (! isscalar (r))
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63 error ("t_test_regression: R must be a scalar");
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64 elseif (! ischar (alt))
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65 error ("t_test_regression: ALT must be a string");
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66 endif
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67
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68 [T, k] = size (x);
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69 if (! (isvector (y) && (length (y) == T)))
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70 error ("t_test_regression: Y must be a vector of length rows (X)");
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71 endif
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72 s = size (rr);
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73 if (! ((max (s) == k) && (min (s) == 1)))
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74 error ("t_test_regression: RR must be a vector of length columns (X)");
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75 endif
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76
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77 rr = reshape (rr, 1, k);
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78 y = reshape (y, T, 1);
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79 [b, v] = ols (y, x);
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80 df = T - k;
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81 t = (rr * b - r) / sqrt (v * rr * inv (x' * x) * rr');
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82 cdf = tcdf (t, df);
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83
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84 if (strcmp (alt, "!=") || strcmp (alt, "<>"))
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85 pval = 2 * min (cdf, 1 - cdf);
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86 elseif (strcmp (alt, ">"))
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87 pval = 1 - cdf;
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88 elseif (strcmp (alt, "<"))
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89 pval = cdf;
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90 else
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91 error ("t_test_regression: the value '%s' for alt is not possible", alt);
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92 endif
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93
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94 if (nargout == 0)
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95 printf ("pval: %g\n", pval);
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96 endif
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97
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98 endfunction